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<p>We present a method for estimating fossil fuel methane emissions using observations of methane and ethane, accounting for uncertainty in their emission ratio. The <span class="inline-formula">ethane:methane</span> emission ratio is incorporated as a spatially and temporally variable parameter in a Bayesian model, with its own prior distribution and uncertainty. We find that using an emission ratio distribution mitigates bias from using a fixed, potentially incorrect emission ratio and that uncertainty in this ratio is propagated into posterior estimates of emissions. A synthetic data test is used to show the impact of assuming an incorrect <span class="inline-formula">ethane:methane</span> emission ratio and demonstrate how our variable parameter model can better quantify overall uncertainty. We also use this method to estimate UK methane emissions from high-frequency observations of methane and ethane from the UK Deriving Emissions linked to Climate Change (DECC) network. Using the joint methane–ethane inverse model, we estimate annual mean UK methane emissions of approximately 0.27 (95 % uncertainty interval 0.26–0.29) <span class="inline-formula">Tg yr⁻¹</span> from fossil fuel sources and 2.06 (1.99–2.15) <span class="inline-formula">Tg yr⁻¹</span> from non-fossil fuel sources, during the period 2015–2019. Uncertainties in UK fossil fuel emissions estimates are reduced on average by 15 % and up to 35 % when incorporating ethane into the inverse model, in comparison to results from the methane-only inversion.</p>